Given a positive integer N, the task is to construct an array consisting of first N natural numbers such that each pair of adjacent elements in the array is a co-prime. If multiple solutions exist, then print any one of them.
Examples:
Input: N = 4
Output: 4 1 3 2
Explanation:
All possible adjacent pairs of the array are { (4, 1), (1, 3), (3, 2) }
Since all adjacent pairs of the array are co-prime, the required output is 4 1 3 2.Input: N = 7
Output: 3 4 5 7 6 1 2
Approach: The idea is to iterate over the range [1, N] using variable i and print the value of i. Following are the observations:
GCD(i, i + 1) = 1
Therefore, for all possible value of i the pair (i, i + 1) are coprime numbers.
Below is the implementation of the above approach:
C++
// C++ program to implement// the above approach#include <bits/stdc++.h>using namespace std;// Function to construct an arrary with// adjacent elements as co-prime numbersvoid ConstArrayAdjacentCoprime(int N){ // Iterate over the range [1, N] for (int i = 1; i <= N; i++) { // Print i cout << i << " "; }}// Driver Codeint main(){ int N = 6; ConstArrayAdjacentCoprime(N); return 0;} |
Java
// Java program to implement// the above approachclass GFG{ // Function to construct an arrary with // adjacent elements as co-prime numbers static void ConstArrayAdjacentCoprime(int N) { // Iterate over the range [1, N] for (int i = 1; i <= N; i++) { // Print i System.out.print(i + " "); } } // Driver Code public static void main (String[] args) { int N = 6; ConstArrayAdjacentCoprime(N); }}// This code is contributed by AnkitRai01 |
Python3
# Python3 program to implement# the above approach# Function to construct an arrary with# adjacent elements as co-prime numbersdef ConstArrayAdjacentCoprime(N): # Iterate over the range [1, N] for i in range(1, N + 1): # Print i print(i, end = " ")# Driver Codeif __name__ == "__main__" : N = 6 ConstArrayAdjacentCoprime(N)# This code is contributed by AnkitRai01 |
C#
// C# program to implement// the above approach using System;class GFG{ // Function to construct an arrary with// adjacent elements as co-prime numbersstatic void ConstArrayAdjacentCoprime(int N){ // Iterate over the range [1, N] for(int i = 1; i <= N; i++) { // Print i Console.Write(i + " "); }}// Driver Codepublic static void Main (){ int N = 6; ConstArrayAdjacentCoprime(N);}}// This code is contributed by susmitakundugoaldanga |
1 2 3 4 5 6
Time Complexity: O(N)
Auxiliary Space: O(1)
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